Validate Power: blocked_i1_2cfr

Design: Blocked RCT, with 2 levels, and randomization done at level 1 (individual level).

Models: Constant treatment effects, fixed treatment effects, and random treatment effects.

Default parameters:

• M = 3
• J = 20
• rho: \(\rho\) = 0.5
• ATE ES = 0.125, 0.125, 0.125
• R2.1: \(R^2_1\) = 0.1, 0.1, 0.1

Parameters by model type:

• Omega: \(\omega_2 = 0\) for constant effects, \(\omega_2\) = 0.1 for fixed and random
• ICC: \(\text{ICC}_2 = 0\) for constant and fixed effects, \(\text{ICC}_2\) = 0.2, 0.2, 0.2 for random effects

Assumptions:

• Two-level design: \(\text{ICC}_3 = 0\), \(\omega_3 = 0\), \(K = 1\)

Power Validation

Varying school size

\(\bar{n}\) = 100

\(\bar{n}\) = 75

\(\bar{n}\) = 50

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6 (This should not affect power!)

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.8, 0.8, 0.8

MDES validation

## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |     0.125     |     0.545     |    0.125    |
## +------------+---------------+---------------+-------------+
## | Bonferroni |     0.125     |     0.379     |    0.125    |
## +------------+---------------+---------------+-------------+
## |     BH     |     0.124     |     0.47      |    0.125    |
## +------------+---------------+---------------+-------------+
## |    Holm    |     0.124     |     0.433     |    0.125    |
## +------------+---------------+---------------+-------------+
## 
## Table: blocked_i1_2c

## 
## 
## +------------+---------------+------------+-------------+
## |    MTP     | Adjusted MDES | min2 Power | Target MDES |
## +============+===============+============+=============+
## |    rawp    |     0.125     |   0.551    |    0.125    |
## +------------+---------------+------------+-------------+
## | Bonferroni |     0.121     |   0.354    |    0.125    |
## +------------+---------------+------------+-------------+
## |     BH     |     0.125     |   0.486    |    0.125    |
## +------------+---------------+------------+-------------+
## |    Holm    |     0.125     |   0.413    |    0.125    |
## +------------+---------------+------------+-------------+
## 
## Table: blocked_i1_2c

## 
## 
## +------------+---------------+---------------+-------------+
## |    MTP     | Adjusted MDES | D1indiv Power | Target MDES |
## +============+===============+===============+=============+
## |    rawp    |     0.125     |     0.463     |    0.125    |
## +------------+---------------+---------------+-------------+
## | Bonferroni |     0.125     |     0.266     |    0.125    |
## +------------+---------------+---------------+-------------+
## |     BH     |     0.126     |     0.373     |    0.125    |
## +------------+---------------+---------------+-------------+
## |    Holm    |     0.126     |     0.333     |    0.125    |
## +------------+---------------+---------------+-------------+
## 
## Table: blocked_i1_2r

## 
## 
## +------------+---------------+------------+-------------+
## |    MTP     | Adjusted MDES | min2 Power | Target MDES |
## +============+===============+============+=============+
## |    rawp    |     0.124     |   0.457    |    0.125    |
## +------------+---------------+------------+-------------+
## | Bonferroni |     0.118     |   0.233    |    0.125    |
## +------------+---------------+------------+-------------+
## |     BH     |     0.125     |   0.381    |    0.125    |
## +------------+---------------+------------+-------------+
## |    Holm    |     0.124     |   0.292    |    0.125    |
## +------------+---------------+------------+-------------+
## 
## Table: blocked_i1_2r

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      J      |     21      |     0.474     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      J      |     21      |     0.439     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_2c

## 
## 
## +------+-------------+-------------+------------+--------------------+
## | MTP  | Sample type | Sample size | min2 power | Target sample size |
## +======+=============+=============+============+====================+
## |  BH  |      J      |     21      |   0.485    |         20         |
## +------+-------------+-------------+------------+--------------------+
## | Holm |      J      |     21      |   0.421    |         20         |
## +------+-------------+-------------+------------+--------------------+
## 
## Table: blocked_i1_2c

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      J      |     21      |     0.474     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      J      |     20      |     0.428     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_2f

## 
## 
## +------+-------------+-------------+------------+--------------------+
## | MTP  | Sample type | Sample size | min2 power | Target sample size |
## +======+=============+=============+============+====================+
## |  BH  |      J      |     20      |   0.484    |         20         |
## +------+-------------+-------------+------------+--------------------+
## | Holm |      J      |     20      |   0.406    |         20         |
## +------+-------------+-------------+------------+--------------------+
## 
## Table: blocked_i1_2f

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      J      |     21      |     0.382     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      J      |     20      |     0.324     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_2r

## 
## 
## +------+-------------+-------------+------------+--------------------+
## | MTP  | Sample type | Sample size | min2 power | Target sample size |
## +======+=============+=============+============+====================+
## |  BH  |      J      |     21      |   0.378    |         20         |
## +------+-------------+-------------+------------+--------------------+
## | Holm |      J      |     20      |   0.296    |         20         |
## +------+-------------+-------------+------------+--------------------+
## 
## Table: blocked_i1_2r